Gamma
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Gamma = (partial^2 V)/(partial S^2) = (partial Δ)/(partial S) — convexity in S, and the rate at which a delta-hedge degrades. Maximal for ATM options near expiry, Gamma_call = dfracφ(d_1)Sσ√(T). Long gamma earns from realised variance (1/2Gamma,(Δ S)^2 per discrete step) but pays theta in calm markets; short gamma is the inverse — large dealers running short-gamma books force mechanical buying as the underlying rises (gamma-driven feedback, notable in S&P 500 dealer-positioning literature).
Gamma in plain English
Gamma measures how *quickly* an option's sensitivity to the stock price changes as the stock moves — it's the 'curviness' of the option's value. Traders who hedge an option constantly rebalance to stay neutral, and gamma tells them how fast that hedge falls out of balance, so bigger gamma means more scrambling to keep up. If you're 'long gamma' you quietly profit whenever the stock jumps around a lot, but you slowly bleed money when markets are calm (that cost is called theta); being 'short gamma' is the reverse — calm is your friend, wild swings hurt. It's like steering a car with very touchy steering: the sharper the response (high gamma), the more constant little corrections you must make to stay in your lane.
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